Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
For researchers in nonlinear wave dynamics, this provides a numerical framework for generating and testing stability of solitary waves in Benjamin-type equations.
The paper numerically studies solitary-wave solutions of generalized Benjamin equations, accurately generating wave profiles with a modified Petviashvili method and analyzing their stability through perturbation and interaction experiments.
This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge-Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves.